Programming is an interdisciplinary practice with applications in both mathematics and computer science. Mathematics concerns rigor, abstraction, and generalization. Computer science predominantly concerns efficiency, concreteness, and physicality. This makes programming a medium for problem solving that mediates between mathematics and computer…

Two philosophical ideas motivate this paper. The first is an answer to the question of what is an appropriate activity for a physicist. My answer is that an appropriate activity is anything where the tools of a physicist enable him or her to make a contribution to the solution of a significant problem. This may be obvious in areas that overlap…

A 100 years-old formula that was given by J. J. Thomson recently found numerous applications in computational electrostatics and electromagnetics. Thomson himself never gave a proof for the formula; but a proof based on Differential Geometry was suggested by Jackson and later published by Pappas. Unfortunately, Differential Geometry, being a…

The opportunity for students to develop formulas that involve tangent lines to a circle and the Pythagorean Theorem and to use approximation and common sense is provided in a suggested distance-to-horizon problem. (MN)

Geometric and algebraic solutions to problems involving reflections of balls on a pool table are presented. The question of whether the ball must eventually enter a pocket is explored. A determination of the number of reflections is discussed. (CW)

Possible ways of mechanization for counting using a binary system are discussed. Shows a binary representation of the numbers and geometric models having eight triples of lamps. Provides three problem sets. (YP)

Four algebra problems and their solutions are presented to illustrate the use of a mathematical theorem. (CW)

The simple physics behind the mechanism of the toy are explained. Experimental and mathematical steps are given that help in understanding the motion of the doll-pair. The geometry of the setup is described. (KR)

Discussed are the geometric patterns formed when two geometric patterns are superimposed. General moire fringes, circular and line gratings, physical applications, and projects for students are described. (CW)

In this instructional guide, a third-level, two-semester mathematics course specifically for the student who plans a career in a vocational field is presented. The course is designed to meet the needs of students with varying mathematical backgrounds and to teach the mathematical skills required by various technical areas. In this practical…

Discusses the geometry, algebra, and logic involved in the solution of a "Mindbenders" problem in "Discover" magazine and applies it to calculations of satellite orbital velocity. Extends the solution of this probe to other applications of falling objects. (JM)

Freudenthal was the founder of realistic mathematics education, in which reality serves as a source of applications and learning. Takes a newspaper article about reproducing a Van Gogh painting using plants in a field to exemplify a rich context problem containing elements of all areas of elementary school mathematics. (MDH)

Presented are two cases of simple geometrical calculations involving the large numbers of atoms that are encountered in two ordinary situations. Included are questions about the spatial implications of the genome and a mole of hydrogen. (CW)

Discusses the calculation of pi by means of experimental methods. Polygon circle ratios, Archimedes' method, Buffon's needles, a Monte Carlo method, and prime number approaches are used. Presents three BASIC programs for the calculations. (YP)

The purpose of this game, intended for grades 7-9, is to enable students to have fun and enjoy mathematics while learning and reinforcing: (1) mathematical concepts and applications; (2) mathematical computations; (3) geometry; and (4) mathematics for daily living. A gameboard and 232 question/answer cards are provided. Rules for play are…